Application of computer algebra methods for investigation of stationary motions of a gyrostat satellite

Abstract

With the help of computer algebra methods, properties of a non-linear algebraic system that determines the equilibrium orientations of a gyrostat satellite moving along a circular orbit were investigated. The main attention is paid to the study of equilibrium orientations of the satellite with given principal central moments of inertia and given gyrostatic torque in special cases, when the projection of the vector of gyrostatic torque is located in one of the principal central planes of inertia of the satellite. Computer algebra method based on the algorithm for the construction of a Gröbner basis were applied to reduce the satellite stationary motion system of nine algebraic equations with nine variables to a single algebraic equation in one variable that determines all the equilibrium orientations of the satellite. Bifurcation curves in the space of system parameters that determine boundaries of domains with a fixed number of equilibria of the satellite were obtained symbolically. A comparative analysis of the effectiveness of different algorithms of Gröbner bases computation in solving the problem was carried out.